I don't believe white's better at all, he is slightly more developed, but theory believes he does not have enough compensation for the pawn. 4. Nc3 was an error for white as well, the b1 knight is usually last to be developed and black often can take advantage of white's esposed king.

I think the 4.Nc3 is ok move. Black should not take the c3 knight due to weakened kingside squares. 4.Nc3 develops nicely i believe. but its all according to a players style

i believe theorie says that in stead of Nc3 0-0 is good

4. Nc3 is a legit move. It's called the Quaade gambit variation. It was suggested by a sea captain and has been played by grand masters such as John Shaw and Simon Williams and many others.

I remember loosely of a famous game that ends in white's win based on this sacrifice, and even the bishop's in f7.

this is the musio gambit whit a few changes

He is still up a piece, and can surpress white's attack.

Bxf7 would be a second unsound piece sack. 8. Bxf7+ Kxf7 9. Qh5+ Kf8 10. Rxf4+ Nf6 and white's attack is nuetralized.

Qf6 is better black wont be allowd to let white take on f4

good move. The immediate blocking of the f file with 8...Nf6 runs into 9. d4! with a very strong threat of e5.

Luckily for you, white didn't play 10. Qg3, with an overwhelming attack.

I disagree, Bxf7+ seems a pinch better.

yes, Ke7 was better, but not by a large amount.

Indeed 14. d4 is much stronger, it's good you can note this.

jackey101, don't take me seriously, but it seems to me that you speak as if you were a GM. I can say that d3 leaves all the black squares to the white's bsb, and the plan could well be Rf3, creating threats of Bg5 and trying to keep black pieces defending (look at this nice a1-h8 diagonal). I don't know if I am right or not, I can suggest it... but how you feel if I tell you "I hope you will be able to notice this"?  )))

14...Nc6 is a better square for the knight. 15. Be3 is good. 15...c5 is an unnecessary pawn move, weakening both b6 and d6.